These are the moments when Gareth Southgate could be forgiven for wondering whether it is time to draw a line through Joe Hart’s international career. This was another personal ordeal for the man who has just lost his place as England’s first-choice goalkeeper. Southgate was here to witness it and, at this rate, there has to be a serious possibility that Hart will be cut adrift from the England squad that goes to Russia for this summer’s World Cup.

What other conclusion can be drawn when the goalkeeping error that led to Peter Crouch, one of Stoke’s substitutes, opening the scoring can hardly be described as a one-off? Indeed, Hart did something very similar in the 3-0 defeat at home to Burnley last month, on the day he was recalled to the side after a long spell in the wilderness. It is becoming a recurring theme and West Ham’s fans were not in the mood to be sympathetic after his latest lapse. There were ironic, unforgiving cheers towards the end whenever Hart gathered the ball without making a mistake.

At least Hart was spared the ignominy of his mistake being the game’s decisive moment and West Ham’s equaliser, courtesy of the fit-again Andy Carroll, helped David Moyes’s team edge another point further away from the relegation places. Stoke, on the other hand, remain in 19th position, having passed up a glorious opportunity to register their first away win since October. Paul Lambert’s side now have only four games to save themselves and still have to play Liverpool after they have hosted Europa League-chasing Burnley on Sunday.

Lambert looked crestfallen afterwards but Stoke’s manager was stretching the truth when he said all the luck had gone against his team. On the contrary, there were three disallowed goals for West Ham in a chaotic second half for the referee, Michael Oliver, in his first game back since the now-infamous Champions League tie between Juventus and Real Madrid, Gianluigi Buffon’s red card and all the unpleasantness that has followed.

Marko Arnautovic had strayed offside before directing in his 55th-minute header and the same player was flagged again when Edimilson Fernandes fired in a shot from 20 yards. This time, Arnautovic was standing directly in Jack Butland’s line of vision and, though Moyes seemed aggrieved at the time, he accepted afterwards it was a fine piece of officiating. West Ham’s manager was less impressed with the decision, in stoppage-time, to penalise Carroll for his challenge on Ryan Shawcross just before another substitute, Javier Hernández, fired in what would almost certainly have been a winner.

It was a dramatic finale to a game that had taken a long time to ignite and, for Carroll, a personal triumph given that he had not played since 4 January and, at one point, was not expected to feature again this season. His goal was expertly taken: he guided in a controlled left-foot volley from Aaron Cresswell’s cross and shifted the mood just as the West Ham fans were preparing, undoubtedly, for another show of loud dissent at the final whistle. Carroll returned to full training only five days before this match and there was an irony that it was two of England’s forgotten men who came up with the goals on the night Southgate was in the crowd to keep tabs on the two goalkeepers.

Moyes made a point afterwards of not being too hard on Hart, restricting himself to saying it was a “surprise” to see the former England No 1 fumbling Xherdan Shaqiri’s shot into Crouch’s path. Moyes also made the point, legitimately, that Hart had made some fine saves in their previous game at Chelsea. Yet this felt like a manager trying not to damage Hart’s confidence any further. The truth, however it is dressed up, was that it was a wretched error from an increasingly accident-prone goalkeeper.

For Stoke, the disappointment was their inability to hold on once they had put themselves in a winning position. The game lived down to expectations during the opening 45 minutes – two ordinary sides huffing and puffing without any real wit or creativity – and it was easy to see why Stoke were averaging under a goal per game this season. Stoke have not managed two goals in a league fixture since January. They have the worst goal difference in the league and it is a problem that needs to be fixed if there is to be a dramatic feat of escapology in the next few weeks.

Lambert argued afterwards that if Stoke had played this well throughout the season Mark Hughes would still be their manager and the team would not be in the bottom three. There was a fair amount of top-spin on that assessment but in one respect it was an improvement – Stoke had lost their previous seven fixtures in London, conceding 26 goals in the process. Ultimately, though, it needed a goalkeeping mistake for them to take the lead and that, for Hart, made this a night that could have serious ramifications for his hopes of going to the World Cup.